Iterative estimation of solutions to noisy nonlinear operator equations in nonparametric instrumental regression
| Autor: | Fabian Dunker, Jan Johannes, Enno Mammen, Thorsten Hohage, Jean-Pierre Florens |
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| Rok vydání: | 2014 |
| Předmět: |
FOS: Computer and information sciences
Polynomial regression Economics and Econometrics Mathematical optimization Statistical assumption Applied Mathematics Nonparametric statistics Mathematics - Statistics Theory Regression analysis Numerical Analysis (math.NA) Statistics Theory (math.ST) Conditional expectation Statistics - Computation Nonparametric regression Methodology (stat.ME) Rate of convergence Convergence (routing) FOS: Mathematics Applied mathematics Mathematics - Numerical Analysis 62G08 (Primary) 62G20 (Secondary) Statistics - Methodology Computation (stat.CO) Mathematics |
| Zdroj: | Journal of Econometrics. 178:444-455 |
| ISSN: | 0304-4076 |
| DOI: | 10.1016/j.jeconom.2013.06.001 |
| Popis: | This paper discusses the solution of nonlinear integral equations with noisy integral kernels as they appear in nonparametric instrumental regression. We propose a regularized Newton-type iteration and establish convergence and convergence rate results. A particular emphasis is on instrumental regression models where the usual conditional mean assumption is replaced by a stronger independence assumption. We demonstrate for the case of a binary instrument that our approach allows the correct estimation of regression functions which are not identifiable with the standard model. This is illustrated in computed examples with simulated data. |
| Databáze: | OpenAIRE |
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